To　implement　less　conservative　than　those　that　ignore　the　difference　between　the　control　and　learning　actions,　an　observer　using　discrete-time　repetitive　control　(RC)　design　schema　was　presented,　based　on　the　two-dimensional　(2D)　system　theory　for　linear　systems　with　uncertainty.　First,　to　describe　both　the　learning　process　occurring　between　two　cycles　and　the　control　behavior　during　a　repetitive　cycle,　a　two　dimensional　discrete-time　model　was　established　accordingly.　Furthermore,　by　rebuilding　the　state　variables,　the　repetitive　controller　designing　was　transformed　to　the　feedback　gain　design　problem.　Thus,　through　linear　matrix　inequality　(LMI),　the　stability　conditions　that　also　gained　quotient　of　repetitive　system　were　obtained.　By　comparison,　the　applicability　of　the　proposal　is　stronger,　significantly　improving　the　robustness　and　tracking　speed.　Test　numerical　simulation　results　show　that　the　method　can　achieve　high　control　accuracy　within　only　a　few　learning　cycles,　and　the　two-dimensional　system　theory　has　broad　application　prospects　in　repetitive　control　design　and　analysis.　©　2017,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.